To calculate the Net Present Value (NPV), we use the following formula for NPV of a project with consistent annual cash inflows:

$\text{NPV} = -C_0 + \sum \frac{C_t}{(1 + r)^t}$

Where:

• $C_0$ is the initial investment (outlay), which is $100,000.
• $C_t$ is the annual cash inflow, which is $19,000.
• $r$ is the discount rate.
• $t$ is the year (1 to 10, since the project lasts 10 years).

a. NPV Calculation at 14% Discount Rate

Given:

• Initial outlay $C_0 = 100,000$
• Annual cash inflow $C_t = 19,000$
• Discount rate $r = 14\%$
• Number of years $t = 10$

The formula for the NPV at a constant cash flow is:

$\text{NPV} = -100,000 + 19,000 \times \left( \frac{1 - (1 + 0.14)^{-10}}{0.14} \right)$

Now let's calculate this step by step:

1. First, calculate the present value factor:

$PVF = \frac{1 - (1 + 0.14)^{-10}}{0.14}$

2. Multiply this present value factor by the annual cash inflow of $19,000.

3. Subtract the initial investment of $100,000 to get the NPV.

Let me compute the exact value for you.

Calculation:

$PVF = \frac{1 - (1.14)^{-10}}{0.14} \approx \frac{1 - 0.2697}{0.14} \approx \frac{0.7303}{0.14} \approx 5.216$

Now, multiply the result by the cash inflows:

$\text{NPV} = -100,000 + 19,000 \times 5.216 \approx -100,000 + 99,104 \approx -896$

So, the NPV at 14% discount rate is approximately -896.

Decision:

Since the NPV is negative ($-896$), the project should not be accepted at a 14% discount rate. A negative NPV indicates that the project's returns do not meet the required return rate of 14%, meaning it would not add value to the company.

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Would you like to proceed with parts b and c, or do you have any questions or need further clarification on part a?

Related questions:

1. How does the NPV change when the discount rate is higher than 14%?
2. How do you interpret a negative NPV for a project?
3. What other methods can be used to evaluate projects besides NPV?
4. How does increasing the project's cash inflows affect its NPV?
5. What are the limitations of using NPV for project evaluation?

Tip: If you have to choose between several projects, always choose the one with the highest positive NPV, as it will increase the firm's value the most.